If you are using Thunderbird, you can try installing the SmtpSelect extension.
If you are trying to solve the more general problem, most (at least the ones I work with) ISPs allow you to authenticate and submit mail to the mail submission port (587). Perhaps this will work for you.
If that still doesn't work, sign up for a gmail account and use gmail's mail submission port (smtp.gmail.com:587) to send your mail out.
If you really don't want to do that, setup some sort of smart script that wakes up every n minutes, checks to see where it is, and reconfigures /etc/hosts or /etc/mail/mailertable to redirect the mail appropriately.
TLS just enables encryption on the smtp session and doesn't directly affect whether or not Postfix will be allowed to relay a message.
The relaying denied message occurs because the smtpd_recipient_restrictions rules was not matched. One of those conditions must be fulfilled to allow the message to go through:
smtpd_recipient_restrictions =
permit_sasl_authenticated
check_recipient_access hash:/etc/postfix/filtered_domains
permit_mynetworks
reject_unauth_destination
To explain those rules:
permit_sasl_authenticated
permits authenticated senders through SASL. This will be necessary to authenticate users outside of your network which are normally blocked.
check_recipient_access
This will cause postfix to look in /etc/postfix/filtered_domains for rules based on the recipient address. (Judging by the file name on the file name, it is probably just blocking specific domains... Check to see if gmail.com is listed in there?)
permit_mynetworks
This will permit hosts by IP address that match IP ranges specified in $mynetworks. In the main.cf you posted, $mynetworks was set to 127.0.0.1, so it will only relay emails generated by the server itself.
Based on that configuration, your mail client will need to use SMTP Authentication before being allowed to relay messages. I'm not sure what database SASL is using. That is specified in /usr/lib/sasl2/smtpd.conf Presumably it also uses the same database as your virtual mailboxes, so you should be able enable SMTP authentication in your mail client and be all set.
Best Answer
SMTP servers also use the SMTP protocol to talk to each other.
Briefly (very briefly) the sending server looks at an address, uses DNS to look up the domain name and find the address of the mail servers at that domain (these are stored as "MX" records in the domain).
The sending server then uses SMTP to contact the mail server at the target domain to send your email, which is done using the exact same procedure as the client used to submit the message in the first place.
You may find this article useful.